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2019•Mathematical logic quarterlyRequires access

Factorials and the finite sequences of sets

Nattapon Sonpanow, Pimpen Vejjajiva

Open publisher page 8 citations

Abstract

Abstract We write for the cardinality of the set of finite sequences of a set which is of cardinality . With the Axiom of Choice ( ), for every infinite cardinal where is the cardinality of the permutations on a set which is of cardinality . In this paper, we show that “ for every cardinal ” is provable in and this is the best possible result in the absence of . Similar results are also obtained for : the cardinality of the set of finite sequences without repetition of a set which is of cardinality .

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What this paper is about

Abstract We write for the cardinality of the set of finite sequences of a set which is of cardinality . With the Axiom of Choice ( ), for every infinite cardinal where is the cardinality of the permutations on a set which is of cardinality . In this paper, we show that “ for every cardinal ” is provable in and this is the best possible result in the absence of . Similar results are also obtained for : the cardinality of the set of finite sequences without repetition of a set which is of cardinality .

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Available abstract

Abstract We write for the cardinality of the set of finite sequences of a set which is of cardinality . With the Axiom of Choice ( ), for every infinite cardinal where is the cardinality of the permutations on a set which is of cardinality . In this paper, we show that “ for every cardinal ” is provable in and this is the best possible result in the absence of . Similar results are also obtained for : the cardinality of the set of finite sequences without repetition of a set which is of cardinality .

Key concepts: Cardinality (data modeling), Mathematics, Cardinal number (linguistics), Set (abstract data type), Axiom of choice, Finite set, Axiom, Combinatorics

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